On the integrability of the 5-dimensional lorenz system for the gravity-wave activity

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2016 American Mathematical Society. We consider the 5-dimensional Lorenz system U′ = −VW + bV Z, V′ = UW − bUZ, W′ = −UV, X′ = −Z, Z′ = bUV + X, where b ∈ R\{0} and the derivative is with respect to T. This system describes coupled Rosby waves and gravity waves. First we prove that the number of functionally independent global analytic first integrals of this differential system is two. This solves an open question in the paper, On the analytic integrability of the 5-dimensional Lorenz system for the gravity-wave activity, Proc. Amer. Math. Soc. 142 (2014), 531-537, where it was proved that this number was two or three. Moreover, we characterize all the invariant algebraic surfaces of the system, and additionally we show that it has only two functionally independent Darboux first integrals.
Original languageEnglish
Pages (from-to)665-679
JournalProceedings of the American Mathematical Society
Volume145
Issue number2
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Darboux first integrals
  • Darboux polynomials
  • Exponential factors
  • Hamiltonian systems
  • Polynomial integrability
  • Rational integrability
  • Weight-homogeneous differential systems

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